1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Water is being poured at the rate of $36 \mathrm{~m}^3 / \mathrm{min}$ into a cylindrical vessel, whose circular base is of radius 3 meters. Then the water level in the cylinder is rising at the rate of

A
$4 \pi \mathrm{~m} / \mathrm{min}$
B
$\frac{4}{\pi} \mathrm{~m} / \mathrm{min}$
C
$\frac{1}{4 \pi} \mathrm{~m} / \mathrm{min}$
D
$\frac{\pi}{4} \mathrm{~m} / \mathrm{min}$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line having direction ratios $1,-4,2$ intersects the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the points $A$ and $B$ resp., then co-ordinates of points A and B are

A
$\mathrm{A}(-8,6,-7)\qquad$ $\mathrm{B}(-6,-2,-3)$
B
$\mathrm{A}(8,6,7)\qquad$ $\mathrm{B(6,2,3)}$
C
$\mathrm{A}(8,6,7)\qquad$ $\mathrm{B}(6,-2,-3)$
D
$\mathrm{A}(7,6,8)\qquad$ $\mathrm{B}(-3,-2,6)$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{x^2-4}{x^4+9 x^2+16} \mathrm{dx}=\tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$ (where c is a constant of integration), then value of $f(2)$ is

A
1
B
2
C
3
D
4
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=2 \hat{i}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}$ are two vectors, then the angle between the vectors $3 \overline{\mathrm{a}}+5 \overline{\mathrm{~b}}$ and $5 \overline{\mathrm{a}}+3 \overline{\mathrm{~b}}$ is

A
$\cos ^{-1}\left(\frac{10}{19}\right)$
B
$\cos ^{-1}\left(\frac{11}{19}\right)$
C
$\cos ^{-1}\left(\frac{13}{19}\right)$
D
$\cos ^{-1}\left(\frac{14}{19}\right)$
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